Description :  Graph minors were initiated by Robertson and Seymour in the 1980s. This project seeks theorems of the form: Let C be a certain class of graphs having elements G and H such that H is contained in G. Then there is a sequence H=G₀, G₁, G₂, ,Gn=G of members of C such that each graph in the sequence is constructed from the preceding one by a simple operation. Theorems of this form are called splitter theorems and provide important tools for both theoretical research and practical applications. This project seeks splitter theorems for several extensive classes of graphs. These extensive classes include the classes of 3- and 4-regular graphs with some fixed girth. New classes that will be studied are the classes of graphs with all vertices of degree 3 or 4 with several connectivity and girth conditions, and the class of 5-regular graphs. For each such class C, a splitter theorem for the subclass of planar graphs in C is also sought. These splitter theorems for planar graphs will provide ways of generating triangulations, quandrangulations, and quintangulations of the sphere with certain degree conditions. I will also seek 3-regular excluded minors for the Klein bottle.

---

Principal Investigator:  Kanno, Jinko  --  Math & Statistics

---

Collaborators:  

---

Funding Agencies:  Board of Regents

---

Amount Awarded:  $58,314

---

Start Period:  06/01/2004

End Period:  06/30/2007